1. Field of the Invention
The invention relates to process control techniques and, more particularly, to an adaptive PID (Proportional, Integral and Derivative) controller that is characterized by parameter values derived from an interpolation of process model parameters.
2. Description of the Related Art
Logic-based, controller-switching strategies have been proposed as a potential approach to the implementation of adaptive process control. See, for example, Morse, F. M. Pait, and S. R. Weller, xe2x80x9cLogic-Based Switching Strategies for Self-Adjusting Control, 33rd IEEE Conference on Decision and Control (December 1994). In general, logic-based controller-switching strategies may be categorized into one of two approaches.
The first approach is predicated on prerouted controller tuning. In principle, prerouted tuning involves sequential evaluation of candidate controllers that are drawn from a prescribed set. The evaluation is complete when a controller is identified that performs satisfactorily. Prerouted tuners are relatively simple to design and impose few requirements on controller structure. However, the advantages of prerouted tuners are overshadowed by intrinsically poor performance with respect to tuning time. That is, an inordinate length of time is often required to select the optimal controller from the prescribed set.
An alternative approach is based on an identifier-based, parameterized controller that consists of two parameter-dependent subsystems, an identifier, the primary function of which is to generate an output estimation error, and an internal controller. The control signal that is fed back to the process is based on a current estimate of the process model. In general, the estimates of the process model are selected from a suitably defined model set. The overall strategy is based on the concept of xe2x80x9ccyclic switching.xe2x80x9d Cyclic switching can be employed with or without process excitation. A worthwhile review and evaluation of this approach to process control adaptation is given by K. S. Narendra and J. Balakrishnan in xe2x80x9cAdaptive Control Using Multiple Models,xe2x80x9d IEEE Transactions on Automatic Control, Vol. 42, No. 2, pp. 177-187 (February 1997). That article discloses an architecture with N identification models operating in parallel. Corresponding to each model is a parameterized controller. At any point in time, one of the models is selected by a switching rule, and the corresponding control input is used to control the process. Models may be fixed or adaptive. The rationale for using fixed models is to ensure that there exists at least one model characterized by parameters sufficiently close to those of the unknown process. The approach yields the desired speed of adaptation, but requires that a significant number of models be constructed. In addition, because fixed models are capable of precisely representing only a finite number of environments, adaptive models must be used to asymptotically improve accuracy.
The practical application of switching strategies poses a number of problems, largely due to the number of models required for a reasonable process approximation. Even in a simple single-input, single-output (SISO) system, a self-tuner can reasonably be expected to necessitate hundreds of fixed models in order to achieve satisfactory performance. The requirement for numerous process models exacerbates exponentially in multivariable systems. More effective solutions require consideration of the specific process model structure and controller type, and suggest the replacement of a simple switching strategy with more elaborate procedures.
A significantly modified approach has been offered by Gendron for a Dahlin controller. See, S. Gendron, xe2x80x9cImproving the Robustness of Dead-Time Compensators for Plants with Unknown of Varying Delay,xe2x80x9d Control Systems 90 Conference (Helsinki 1990). Gendron therein describes a simple first-order-plus-dead-time process model, according to which process adaptation is effected exclusively through dead time variation. Rather than relying on simple switching, the controller assumes a process model that is derived a weighted sum of models that are characterized by disparate dead times. Each model in the set generates a prediction of the process output, and the corresponding weight is adjusted automatically as a simple function of the prediction error. The concept has been extended to incorporate into a Dahlin controller both process gain and dead time uncertainty in the Dahlin controller construct.
In general, there exist two prominent approaches for designing a PID adaptive controller. To wit: the direct approach, and the indirect, or identifier-based, approach. As has been indicated above, because the identifier-based approach is advantageous for switching strategies, the subject invention generally pursues this approach for the design of an adaptive switching PID controller. Because there appears to be no art related to the switching of PID controllers, the present invention is deemed most nearly related to the classical identifier-based, adaptive PID controller. The result is an adaptive PID controller, coupled with a Recursive Least Squares (RLS) estimator, that tracks changes in the model parameters. Typical problems associated with recursive identifiers are known to include the selection of initial parameters, insufficient excitation, filtering, parameters wind-up, and sluggish parameter tracking speed. It is known that performance improvements may be obtained by simplifying the process model. A worthwhile example of this solution is given by Astrom and Hagglund in xe2x80x9cIndustrial Adaptive Controllers Based on Frequency Response Techniques,xe2x80x9d Automatica, Vol. 27, No. 4, pp. 599-609 (1991). The controller described therein is designed to perform adaptation in the frequency domain, and performs tuning in response to setpoint changes and natural disturbances. A specific tuning frequency is selected by applying band-pass filters to the process input and output. The frequency of the filters is set by the auto-tuner (tuner-on-demand). The auto-tuner defines the ultimate period using a relay oscillation technique, prior to adaptive tuner operation. The adaptive tuner defines the process gain for the tuning frequency using a simplified RLS estimator. The tuner has the capability to easily track changes in a process gain. However, when a change in a dead time or in a time constant is encountered, the point tracked no longer exhibits a xe2x88x92xcfx80 phase, and controller tuning becomes inaccurate. It is known that tuning can be improved significantly by applying several tuning frequencies and by using an interpolator to define a frequency with phase xe2x88x92xcfx80. Alternatively, it is possible to instantly operate with only one tuning frequency and adjust that frequency after each tuning cycle to track a phase xe2x88x92xcfx80. Both designs accommodate subsequent set point changes and natural disturbances and may inject external excitations at the controller output or at the setpoint input. Although such tuners do not exhibit the constraints of the previous technique, they are significantly more complex.
A more serious detriment of both designs is the reliance on a relatively primitive adaptive model that recognizes only two parameters: Ultimate Gain and Ultimate Period. A tuner model of this design is suitable for Ziegler-Nichols tuning or some cognate modifications, but will not satisfy the requirements of many applications where Internal Model Control (IMC) or Lambda tuning are preferred. A simple RLS identifier may be used to determine static gain for the feedforward control. However, that approach does not provide the process feedforward dynamics required for adequate feedforward control. In addition, because feedforward signals are load disturbances, and perturbation signals can not be injected as they may into the feedback path, the approach suffers the problem of insufficient excitations.
A more sophisticated solution to feedforward adaptation is disclosed in U.S. Pat. No. 5,043,863, xe2x80x9cMultivariable Adaptive Feedforward Controller,xe2x80x9d to Bristol and Hansen. That patent describes a differential equation process model designed to include load disturbances. The model is periodically updated based on process data. Disturbances are characterized by moment relations and by control relations that are achieved by projection methods. In general, the solution is very complex and requires significant excitations, much the same RLS identification. The solution is suitable only for feedforward control and is inapplicable to an adaptive controller with feedback.
Accordingly, what is desired is an adaptive controller that surmounts the above-identified shortcomings that are exhibited by known approaches to adaptive control. Specifically, what is required is a uniform solution to feedback and feedforward adaptive PID control. Salient objectives addressed by the inventive Adaptive Feedback/Feedforward PID Controller include: shorter adaptation time, minimization of constraints imposed on the use of PID tuning rules, simplicity of design, and attainment of adaptation with reduction in process excitation.
The above and other objects, advantage and capabilities are realized in one aspect of the invention in a method of adaptively designing a controller in a process control system. According to the method, a set of models for the process is established. Each of the models is characterized by a plurality of parameters, and, for each model, each of the parameters has a respective value that is selected from a set of predetermined initialization values corresponding to the parameter. Evaluation of each of the models includes a computation of a model-squared error, or norm. The norm value is assigned to every parameter value represented in the model that is evaluated. As repeated evaluations of models are conducted, an accumulated norm is calculated for each parameter value. The accumulated norm is the sum of all norm that have been assigned to the parameter value in the course of model evaluations. Subsequently, an adaptive parameter value is calculated for each parameter. The adaptive parameter value is a weighted average of the initialization values assigned to the respective parameters. The controller is then redesigned in response to the adaptive parameter values.
Another aspect of the invention is embodied in a controller for use in controlling a process. The controller is characterized by controller parameters that are derived from adaptive process parameter values that are established according to the steps:
(i) establishing a set of models for the process, wherein each of the models is characterized by a plurality of parameters and, in each model, the value of each parameter is selected from a set of predetermined initialization values assigned to that parameter;
(ii) evaluating each of the models, whereby a model squared error, El(t), is determined in the course of the evaluation of each of the models;
(iii) assigning a norm to each parameter value represented in an elevated model;
(iv) for each parameter, establishing an adaptive parameter value that is a weighted average of the values populating the set of initialization values assigned to the respective parameter; and
(v) imparting adaptive controller parameter values to the controller, wherein the adaptive controller parameter values are derived from the adaptive process parameter values.
Another manifestation of the invention is comprehended by a system for tuning a process controller. The system may be implemented in either hardware software, or a combination thereof. The system comprises a models component having an input coupled to a process input. The models component comprises a plurality of process models, and each of the models is characterized by a plurality of parameters that have parameter values selected from a set of predetermined initialization values assigned to the respective parameter. An error generator has a first input coupled to an output of the models component and a second input coupled to the process output. The error generator generates a model error signal that represents the difference between the output of a model and the output of the process. A models evaluation component has an input coupled the an output of the error generator for computing a model squared error corresponding to a model for attributing the model squared error to parameter values represented in the model. A parameter interpolator has an input coupled to an output of the models evaluation component for calculating an adaptive process parameter value for parameters represented in a model. A controller redesign component has an input coupled to an output of the parameter interpolator and an output coupled to a controller. The controller redesign component imparts adaptive controller parameter values to a controller upon conclusion of an adaptation cycle. The adaptive controller parameter values are derived from the adaptive process parameter values that are calculated.
The invention is also embodied in an adaptive feedback/feedforward (FB/FC) controller that comprises a feedback controller (FBC) input node, and FBC output node, a process input node coupled to the FBC output node, a process output node coupled to the FBC input node, and an error node. An FBC is coupled between the FBC input node and the FBC output node. A models component has an input coupled to the process input node and comprises a plurality of controller models, wherein each of the models is characterized by a plurality of parameters. The parameters have values selected from sets of predetermined initialization values compiled for each of the parameters. An error generator has a first input coupled to an output of the models component and a second input coupled to the process output node. The error generator generates, at an error node, a model error signal that represents the instantaneous difference between the output of a model and the output of the process. A models evaluation has an input coupled to the error node and operates to compute a model squared error corresponding to a model. The model squared error is attributed to parameter values represented in a corresponding model. A parameter interpolator has an input coupled to an output of the models evaluation component for calculating adaptive parameter values to be associated with parameters represented in a model. A controller redesign component is coupled to the output of the parameter interpolator and imparts the adaptive parameter values to a controller upon conclusion of an adaptation cycle. Elements of the invention, including but not necessarily limited to, the models component, error generator, models evaluation component, parameter interpolator and controller redesign component, may be instantiated in hardware, software, and/or an appropriate combination thereof. In a control system that incorporates feedforward as well as feedback control, the models component includes a plurality of feedforward controller (FFC) models as well as FBC models, and the parameters that characterize the FBC models may be different from the parameters that characterize the FFC models. Furthermore the parameter interpolator may be partitioned into a FFC parameter interpolator and a FBC parameter interpolator. Consequently, the controller redesign component will be similarly partitioned to impart FBC adaptive parameters and FFC adaptive parameters to the respective controllers.
The invention also contemplates circumstances according to which not all process parameters will be subject to adaptation in a given adaptation cycle. Limited adaptation is indicated when there is reason to believe that only one, or at least not all, the process parameters have changed. For example, it may be assumed that because of the amount of time elapsed since the most recent adaptation cycle, the process Gain parameter has drifted, while other process parameters remain substantially constant. Therefore, the process supervisor, described below, will initiate an adaptation cycle, but will cause only the process Gain parameter to be adapted. The process controller is then redesigned in response to the adapted process Gain parameter. Accordingly, the invention also inheres in a method of adaptive controller whereby, as above, a model set is compiled for the process, and each of the models is evaluated, that is, a corresponding model squared error is computed for each model. An adaptive (Gain) parameter value is calculated based on the weighted sum of each of the predetermined initialization parameter values. The initialization values are weighted by Normalized Fitness factors. With an adaptive process (Gain) parameter calculated, the controller is redesigned accordingly.